Lesson 1 - 2D Acceleration

2D Acceleration explores the relationship between acceleration and velocity in linear motion and two-dimensional motion, including projectile and circular motion.

Prerequisites

Students should be familiar with the definition of velocity and acceleration.

Learning Outcomes

Students will be able to define velocity as a change in position during a time interval and acceleration as a change in velocity during a time interval. Students will also explore the relationship between acceleration and velocity for linear motion, projectile motion, and circular motion.

Instructions

Students should understand the applet functions that are described in Help and ShowMe. The applet should be open. The step-by-step instructions in the following text are to be done in the applet. You may need to toggle back and forth between instructions and applet if your screen space is limited.

Contents

  1. Basic Definitions and Terms
  2. Exercises and Challenges

1. Basic Definitions and Terms

space shuttle

When the velocity of a moving object changes, it is said to have undergone acceleration. For example, during the space shuttle launch the rocket engines provide an acceleration that changes the velocity of the shuttle. The concept of acceleration, however, is not always that simple. For example, the direction of the acceleration vector is the direction of the change in velocity, which may not be in the same direction as the velocity itself.

This lesson will explore and illustrate the relationship between velocity and acceleration.

Recall the following definitions that will be required to complete the exercises and challenges that follow.

Velocity is a measure of the change in position during a given time interval. Therefore, velocity is a measure of the rate of change of position.
Expressed as an equation:

velocity=distance/time

Quantity Symbol SI Unit
velocity velocity vector m/s
change in position displacement vector m
time interval Δt s

* delta "Δ" notation means "change".

Acceleration is a measure of the change in velocity during a given time interval. Therefore, acceleration is a measure of the rate of change of velocity.

Expressed as an equation:

acceleration=velocity/time

Quantity Symbol SI Unit
acceleration acceleration vector m/s2
change in velocity velocity vector m/s
time interval Δt s

* delta "Δ" notation means "change".

Both velocity and acceleration are vector quantities. This means they have both size (magnitude) and direction which defines them.

2. Exercises and Challenges

Complete Exercises 1 and 2 without using the applet.

exercise 1

A cross-country runner travels at a steady speed and covers 10 km in 25 minutes. How fast did she run (express in both m/s and km/h)? Is there enough information to completely specify her velocity? Explain.
exercise 2

Bob was heading due east on his skateboard at a speed of 10.0 m/s when he hit sand. He stayed on the board and stopped 4.0 seconds after first entering the sand. What was his acceleration? In what direction did the acceleration point?
The applet will now be used to illustrate the differences and similarities between velocity and acceleration. For the following exercises you will need to adjust either the initial velocity or acceleration vectors. This can be done by clicking on the desired vector and dragging it out. For example:

adjust velocity vector Click and drag the velocity vector to change the initial velocity of the object.

adjust acceleration vector Click and drag the acceleration vector at any time to adjust the acceleration of the object.
exercise 3

Set up the applet to simulate each of the following situations. Using the terms "speed up", "slow down" and "change direction", describe the initial motion of the moving object when:

  1. acceleration is in the opposite direction of the initial velocity.

    a opposite v

  2. acceleration is in the same direction as the initial velocity.

    a same as v

  3. acceleration is at right angles to the initial velocity.

    a right to v

exercise 4

According to the figure below, both the velocity and acceleration have a negative direction. Comparing the figure below to your observations from Exercise 3b, does a negative acceleration necessarily mean to "slow down"? What orientation of velocity and acceleration will cause something to initially slow down? What orientation of velocity and acceleration will cause something to initially speed up?

acceleration and velocity in same direction
exercise 5

On the applet, set the initial acceleration and velocity as shown on the figure below. Run the simulation and observe the motion of the object. Explain what happened to the direction of the initial velocity and suggest a common type of motion that follows a parabolic path similar to the one you observed.

acceleration and velocity at angles to one another
exercise 6

Use the applet to "simulate" the motion of Bob in Exercise 2. What would happen to Bob's velocity if he continued to accelerate even after he came to rest?






exercise 7

Set up the applet to simulate the case of a baseball which is thrown straight up.

  1. Draw the initial velocity vector:

    box



  2. Draw the constant acceleration vector:

    image



  3. Is there a point on the trajectory where the ball has zero velocity? Where on the trajectory does this occur?




  4. Is there a point on the trajectory where the ball has zero acceleration? Explain.
exercise 8

On the applet, add some obstacles by clicking the "Obstacles" check box (checkbox obstacles). By adjusting only the acceleration, try to move the object over each obstacle starting with obstacle 0 and ending with obstacle 4. Does the acceleration "steer" the object? Explain.






exercise 9

Using the applet, try to get the ball to travel in a circular path. How do you have to adjust the acceleration to accomplish this?




exercise 10

In what direction does the acceleration need to point in order to keep an object traveling in a perfectly circular path?






exercise 11

Is it possible for an object to accelerate and yet neither speed up nor slow down? Explain.





exercise 12

Based on your observations from all the previous exercises it is clear that acceleration will change the magnitude and/or direction of the velocity. With this in mind, complete the following list of "accelerators" common to all vehicles.

  1. the engine (gas pedal)
  2. the brakes (brake pedal)
  3. ___________________

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Last Updated: June 16, 2004